1. Technical Field
The present invention relates to a resonator element, a resonator, an oscillator, an electronic device, and a frequency adjustment method.
2. Related Art
In a resonator having a vibrating arm, a resonator element is known in which a vibrating arm vibrates in the thickness direction of the vibrating arm (such a mode of vibration is an out-of-plane mode) rather than vibrating in an in-plane mode. This resonator element generally has an odd number of vibrating arms. When the resonator element has three or more vibrating arms, adjacent vibrating arms perform walk-mode vibration in which they repeatedly vibrate alternately in opposing directions.
Adjustment of the frequency of a tuning-fork type resonator that vibrates in an in-plane mode is performed by providing a weight on a plane in the vibration direction of the tip end of a vibrating arm and irradiating the weight with laser light or the like to remove a part of the weight. This method performs frequency adjustment by removing a part of the weight to decrease the weight of the vibrating arm, thus sequentially increasing the frequency (see JP-A-2003-318685, for example).
In contrast, the frequency of a resonator that vibrates in an out-of-plane mode is proportional to the thickness in the vibration direction of a vibrating arm and is inversely proportional to the square of the length of the vibrating arm. Therefore, adjustment of the frequency is performed by adding a weight to the side surfaces of a vibrating arm rather than adding the weight to the surfaces defining the thickness of the vibrating arm and irradiating the weight with laser light to remove apart of the weight on the side surfaces.
When a resonator vibrating in an out-of-plane mode is miniaturized, since the length of the vibrating arm decreases, it is necessary to make the vibrating arm thinner in order to obtain the same frequency.
However, it is difficult to add a weight on side surfaces of a thin vibrating arm to perform frequency adjustment of a resonator element. Moreover, even when the weight can be added to the side surfaces of the vibrating arm, it is very difficult to irradiate the side surfaces with laser light to remove a part of the weight. It is desirable that frequency adjustment of a resonator that vibrates in the out-of-plane mode is performed easily and with high accuracy.
In a resonator element that vibrates in the out-of-plane mode, similarly to a resonator element that vibrates in the in-plane mode of the tuning-fork type, when performing frequency adjustment by adding or removing a film in the thickness direction of the vibrating arm, it is necessary to consider changes in the thickness as well as just a weight effect. For this reason, it was considered difficult to perform the frequency adjustment by adding or removing a film in the thickness direction of the vibrating arm in a resonator that vibrates in the out-of-plane mode.
The present inventor has made an observation using a resonator element that vibrates in the out-of-plane mode and has one vibrating arm on a base portion thereof as a model and performed a simulation on the changes in frequency when a gold (Au) film is formed on one surface of the vibrating arm and removed from the tip end side of the vibrating arm.
According to the observation, when a mass portion such as a metal film or an insulating film formed on the vibrating arm is removed from the tip end side thereof, the frequency sequentially increases, and the frequency change becomes zero at approximately the central portion of the vibrating arm. When the mass portion such as the metal film or the insulating film is further removed towards the base portion, the frequency sequentially decreases.
Given the above, the present inventor has discovered a fact that the boundary at which the direction of the change in the frequency changes is present approximately near the center in the longitudinal direction of the vibrating arm and has concluded that the frequency of the resonator can be adjusted using this phenomenon. Particularly, near the center of the vibrating arm, the changes in frequency with the removal of the mass portion such as the metal film or the insulating film are small, and high-accuracy frequency adjustment can be expected.
However, it is necessary to form an excitation electrode in the vibrating arm so as to extend from the base portion to a length of about ½ of the length of the vibrating arm in order to excite the vibrating arm. This is because unless the excitation electrode is formed to a length of about at least ½ of the vibrating arm, the excitation efficiency deteriorates and the CI value increases. Thus, it is difficult to obtain favorable vibration properties in the resonator element.
For this reason, when a mass portion is provided closer to the tip end side than the half-length portion of the resonator element, a variation of the frequencies increases with the removal of the metal film or the insulating film, and fine tuning thereof is difficult. Thus, there is a problem in that it is not possible to adjust the frequencies with high accuracy.
Moreover, the mass portion can be provided near the center in the longitudinal direction of the vibrating arm by forming the mass portion on a surface opposite the excitation electrode, and fine tuning of the frequencies is possible. However, in this case, since the metal film or the insulating film is removed, for example, by irradiating it with laser light, the mass portion may cause damage to the excitation electrode on the rear surface. Moreover, if the excitation electrode is damaged, the vibration properties of the resonator element deteriorate.
Given the above, it is desirable to have a resonator element which enables high-accuracy frequency adjustment without deteriorating the vibration properties of the resonator element.